I am looking for steps to answer question 1. **TJ, Inc. Nut Mix Distribution Analysis****Introduction:**TJ, Inc. distributes three nut mixes—Regular Mix, Deluxe Mix, and Holiday Mix—to grocery chains in the Southeast. These mixes use varying percentages of five types of nuts.**Nut Shipments:**TJ, Inc. prepared for the fall season by purchasing the following amounts of nuts:| Type of Nut | Shipment Amount (pounds) ||-------------|--------------------------|| Almond | 6000 || Brazil | 7500 || Filbert | 7500 || Pecan | 6000 || Walnut | 7500 |**Nut Mix Composition:**- **Regular Mix:** 15% almonds, 25% Brazil nuts, 25% filberts, 10% pecans, 25% walnuts- **Deluxe Mix:** 20% of each nut type- **Holiday Mix:** 25% almonds, 15% Brazil nuts, 15% filberts, 25% pecans, 20% walnuts**Profit Contribution:**An accountant determined the profit per pound for each mix type:- Regular Mix: $1.85- Deluxe Mix: $2.10- Holiday Mix: $2.15These figures exclude specific nut costs due to market variability.**Customer Orders:**Orders received thus far:| Type of Mix | Orders (pounds) ||-------------|-----------------|| Regular | 10000 || Deluxe | 3000 || Holiday | 5000 |**Demand and Strategy:**TJ, Inc. anticipates more orders than the available supply. The company aims to maximize profits using the current nut supply and will donate any excess to the Free Store.**Managerial Report Objectives:**Prepare a report including:1. **Optimal Product Mix:** Determine best product mix for maximum profit.2. **Almond Purchase Decision:** Advise on buying additional 500 pounds of almonds for $500.3. **Maximizing Profit Contribution:** Provide strategies for profit increase, if orders are unmet.**Analysis Requirement:**Analyze and present strategies to TJ, Inc.'s president, emphasizing optimal product mix and financial recommendations.

There are 3 products:Regular MixDeluxe MixHoliday Mix5 types of nuts are required to make the above 3 products:Types of NutsRegular MixDeluxe MixHoliday MixAvailabilityAlmonds15%20%25%6000Brazil25%20%15%7500Filbert25%20%15%7500Pecan 10%20%25%6000Walnut25%20%20%7500The profit contribution per pound are:Regular Mix = $1.85Deluxe Mix = $2.10Holiday Mix = $2.15Decision VariablesLet's denote:R = pounds of Regular Mix to produceD = pounds of Deluxe Mix to produceH = pounds of Holiday Mix to produceObjective FunctionThe objective is to maximize the profit. The profit contribution per pound is $1.85 for the Regular Mix, $2.10 for the Deluxe Mix, and $2.15 for the Holiday Mix.So, the objective function is:Maximize Z = 1.85R + 2.10D + 2.15HConstraintsThe constraints are based on the availability of each type of nut and the orders already received. The constraints are as follows:Almond: 0.15R + 0.20D + 0.25H <= 6000Brazil: 0.25R + 0.20D + 0.15H <= 7500Filbert: 0.25R + 0.20D + 0.15H <= 7500Pecan: 0.10R + 0.20D + 0.25H <= 6000Walnut: 0.25R + 0.20D + 0.20H <= 7500R >= 10000D >= 3000H >= 5000R,D,H >= 0 (Non-negativity constraint)Formulate the problem in Excel as shown below:Now go to DATA TAB in Excel and Click on SOLVER. Fill the parameters as shown below:Click on Solve and the following message will be displayed indicating that Solver has found a solution:The results are depicted below:The optimal product mix isR = pounds of Regular Mix to produce = 17500D = pounds of Deluxe Mix to produce = 10625H = pounds of Holiday Mix to produce = 5000The above optimal solution will give the optimal production quantity for each type of mix to maximize the profit.The total profit contribution from the optimal product mix is $65437.5The total profit contribution from the existing orders:- Regular Mix: 10,000 pounds * $1.85/pound = $18,500- Deluxe Mix: 3,000 pounds * $2.10/pound = $6,300- Holiday Mix: 5,000 pounds * $2.15/pound = $10,750Total profit contribution from existing orders: $18,500 + $6,300 + $10,750 = $35,550The optimal product mix isRegular Mix = 17500Deluxe Mix = 10625Holiday Mix = 5000The total profit contribution from the optimal product mix is $65437.5Total profit contribution from existing orders = $35,550

Business

Operations Management

TJ, Inc., makes three nut mixes for sale to grocery chains located in the Southeast. The three mixes, referred to as the Regular Mix, the Deluxe Mix, and the Holiday Mix, are made by mixing different percentages of five types of nuts. In preparation for the fall season, TJ, Inc., purchased the following shipments of nuts: Type of Nut Almond Brazil Filbert Pecan Walnut Shipment Amount (pounds) 6000 7500 7500 6000 7500 The Regular Mix consists of 15% almonds, 25% Brazil nuts, 25 % filberts, 10% pecans, and 25% walnuts. The Deluxe Mix consists of 20% of each type of nut, and Holiday Mix consists of 25% almonds, 15% Brazil nuts, 15% filberts, 25% pecans, and 20% walnuts. An accountant at TJ, Inc., analyzed the cost of packaging materials, sales price per pound, and so forth, and determined that the profit contribution per pound is $1.85 for the Regular Mix, $2.10 for the Deluxe Mix, and $2.15 for the Holiday Mix. These figures do not include the cost of specific types of nuts in the different mixes because that cost can vary greatly in the commodity markets. Customer orders already received are summarized here: Type of Mix Regular Deluxe Holiday Orders (pounds) 10000 3000 5000 Because demand is running high, TJ, Inc., expects to receive many more orders than can be satisfied. TJ, Inc., is committed to using the available nuts to maximize profit over the fall season; nuts not used will be given to the Free Store. Even if it is not profitable to do so, the president of TJ, Inc., indicated that the orders already received must be satisfied. Managerial Report Perform an analysis of the TJ, Inc. product mix problem. Prepare a summary report of your findings for TJ, Inc.'s president. Be sure to include information and analysis on the following: 1. The optimal product mix and the total profit contribution 2. A recommendation as to whether TJ, Inc., should purchase an additional 500 pounds of almonds for $500 from a supplier who overbought 3. Recommendations on how profit contribution could be increased (if at all) if TJ, Inc., does not satisfy all existing orders